In this film, Andrea Arnold has demonstrated her mastery and fluency in the social-realist idiom, and simply makes it fizz with life. Having now watched Fish Tank a second time, I am more exhilarated than ever by Arnold's idealism, and in a movie marketplace where so much is vapidly cynical, this is a mistral of fresh air. Arnold finds a way into the fashionable notion of a "Broken Britain", but in place of the pundits' dismay and contempt, she offers tenderness and hope. If Ken Loach were ever somehow called on constitutionally to nominate a successor, it would surely have to be Arnold. She's got the grit; she has Loach's humanism and optimism and she has a happy knack of getting great performances out of her cast, particularly from Michael Fassbender, who proves that he's not just sex on a stick – he's complexity and vulnerability on a stick as well. Added to this, Arnold and her cinematographer, Robbie Ryan, conjure some glorious, almost Turner-ish images of the Essex countryside, with its racing summer skies.

At the centre of the story is newcomer Katie Jarvis, playing Mia, a tricky, lairy 15-year-old in trouble with the social services for breaking a girl's nose after a contretemps in one of the windswept municipal canyons lying between tower blocks. She has inherited from her mum, played by Kierston Wareing, a stroppy insecurity and a nascent fondness for the booze. The family dog is actually called Tennent's. Mia has a feisty younger sister, Tyler – a scene-stealer of a performance from Rebecca Griffiths – who is always winding Mia up with shrill threats to "tell on her". There is no dad in the picture. Mia has just one interest in life: urban dance, and she isn't too bad, but the moves she practises are moody, introverted and subdued, rather like the dancer herself.

Their torpid lives are disrupted when Mia's mother miraculously gets a new boyfriend, Connor: and Fassbender gives his best performance yet. Connor is funny, sexy, confident and utterly relaxed where everyone else appears clenched with resentment. Noticeably articulate, Connor appears to come from a marginally more middle-class world and he is also, tellingly, a breadwinner. Mia rifles through his wallet while he's upstairs with her mum and instead of immediately nicking the cash, she gazes fascinated at his payslips: a man who actually works for a living. How many of those has she ever met?

Without consciously realising it, Mia is hoping that Connor could be a father-figure, and both sisters are secretly thrilled when he takes them all out for a drive in the country, and shows them how he can catch a fish with his bare hands. While her mother and sister cringe on the riverbank, Mia wades out into the cold, slimy water to help him and Tyler squeaks: "Is it minging?"

No, it is not minging. It is sensual and exciting, an exotic experience such as Mia has never known. And it marks the decisive point at which Connor and Mia's relationship drifts past being that of a quasi-father and daughter. Connor even takes an interest in her dancing, and casually lends her his expensive camcorder to tape an audition for a local competition, trusting that he will get it back. "You dance like a black," he tells her, with studied, flirtatious insolence. "I mean it as a compliment."

Mia has an enormous, poignant capacity for love, but she has never received any, certainly not from a damaged mother, whose one moment of intimacy with her daughter comes when she ferociously tells Mia that she was thinking of having her aborted. So she has no idea how to express or manage love and it is her muddled, suspicious longing for the safety and comfort of a father's care that makes the situation so explosive. As for Connor, it is far from clear how much baggage he has: he moves in to Mia's mum's flat because he says his own mother has thrown him out and often has to take calls from his "mum", but what is really going on? It becomes all too clear that if Mia has her own issues about family, then so does Connor – whose secrets are shabbier and more poisonous than either Mia or her mother could have realised.

The situation heralds an unwatchably tense finale as Mia's adoration turns into anger and then a determination to survive, to outgrow her surroundings, and to forgive. Arnold shows us that what makes the relationship between Mia and Connor so transgressive is not their obvious sexual attraction but their quite genuine, if thwarted and delusional longing to be father and daughter.

Jarvis has given a wonderfully honest and open performance to be compared with David Bradley in Kes, or Émilie Dequenne in the Dardenne brothers' Rosetta. Her relationship with Fassbender is what gives the film its beating heart.